Plateau Stein Manifolds
Differential Geometry
2018-11-13 v1
Abstract
We study/construct (proper and non-proper) Morse functions on complete Riemannian manifolds, the level hypersurfaces of which have positive mean curvatures at all non-critical points. We show, for instance, that if a complete Rieannin manifold admits no such (not necessarily proper) function, then it contains a (possibly, singular) complete (possibly, compact) minimal hypersurface of finite volume.
Keywords
Cite
@article{arxiv.1811.04316,
title = {Plateau Stein Manifolds},
author = {Misha Gromov},
journal= {arXiv preprint arXiv:1811.04316},
year = {2018}
}